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arXiv · 1812.07364

A right inverse operator for $\operatorname{curl}+λ$ and applications

Briceyda B. Delgado·Vladislav V. Kravchenko
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Abstract

A general solution of the equation $\operatorname{curl}\vec{w}+λ\vec {w}=\overrightarrow{g},\,λ\in\mathbb{C},\,λ\neq0$ is obtained for an arbitrary bounded domain $Ω\subset\mathbb{R}^{3}$ with a Liapunov boundary and $\overrightarrow{g}\in W^{p,\operatorname{div}}\left( Ω\right) =\left\{ \overrightarrow{u}\in L^{p}\left( Ω\right) :\,\operatorname{div}\overrightarrow{u}\in L^{p}\left( Ω\right) ,\,1<p<\infty\right\} $. The result is based on the use of classical integral operators of quaternionic analysis. Applications of the main result are considered to a Neumann boundary value problem for the equation $\operatorname{curl}\vec{w}+λ\vec {w}=\overrightarrow{g}$ as well as to the nonhomogeneous time-harmonic Maxwell system for achiral and chiral media.

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Briceyda B. Delgado, Vladislav V. Kravchenko. 2018-12-18. A right inverse operator for $\operatorname{curl}+λ$ and applications. https://arxiv.org/abs/1812.07364

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